interatomic 0.5.0

Library for calculating inter-particle interactions
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252

// Copyright 2023 Mikael Lund
//
// Licensed under the Apache license, version 2.0 (the "license");
// you may not use this file except in compliance with the license.
// You may obtain a copy of the license at
//
//     http://www.apache.org/licenses/license-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the license is distributed on an "as is" basis,
// without warranties or conditions of any kind, either express or implied.
// See the license for the specific language governing permissions and
// limitations under the license.

//! # Electric multipole interactions
//!
//! This module provides tools for calculating the two-body interaction energy between
//! electric multipole moments, such as monopoles, dipoles, quadrupoles etc.

use crate::{twobody::IsotropicTwobodyEnergy, Cutoff};
use coulomb::{
    pairwise::MultipoleEnergy,
    permittivity::{ConstantPermittivity, RelativePermittivity},
};
#[cfg(feature = "serde")]
use serde::Serialize;
use std::fmt::{Debug, Display};

/// Monopole-monopole interaction energy
#[derive(Clone, PartialEq, Debug)]
#[cfg_attr(feature = "serde", derive(Serialize))]
pub struct IonIon<T: MultipoleEnergy> {
    /// Charge number product of the two particles, z₁ × z₂
    #[cfg_attr(feature = "serde", serde(rename = "z₁z₂", alias = "z1z2"))]
    charge_product: f64,
    /// Potential energy function to use.
    #[cfg_attr(feature = "serde", serde(skip))]
    scheme: T,
    /// Relative dielectric constant of the medium
    permittivity: ConstantPermittivity,
}

impl<T: MultipoleEnergy + Display> Display for IonIon<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}, {}", self.scheme, self.permittivity)
    }
}

impl<T: MultipoleEnergy> coulomb::DebyeLength for IonIon<T> {
    fn kappa(&self) -> Option<f64> {
        self.scheme.kappa()
    }
    fn set_debye_length(&mut self, debye_length: Option<f64>) -> Result<(), coulomb::Error> {
        self.scheme.set_debye_length(debye_length)
    }
    fn debye_length(&self) -> Option<f64> {
        self.scheme.debye_length()
    }
}

impl<T: MultipoleEnergy> RelativePermittivity for IonIon<T> {
    fn permittivity(&self, _temperature: f64) -> Result<f64, coulomb::Error> {
        Ok(f64::from(self.permittivity))
    }
    fn set_permittivity(&mut self, permittivity: f64) -> Result<(), coulomb::Error> {
        self.permittivity = ConstantPermittivity::new(permittivity);
        Ok(())
    }
}

impl<T: MultipoleEnergy> IonIon<T> {
    /// Create a new ion-ion interaction
    pub const fn new(charge_product: f64, permittivity: ConstantPermittivity, scheme: T) -> Self {
        Self {
            charge_product,
            permittivity,
            scheme,
        }
    }
}

impl<T: MultipoleEnergy + Debug + Clone + PartialEq + Send + Sync> IsotropicTwobodyEnergy
    for IonIon<T>
{
    /// Calculate the isotropic twobody energy (kJ/mol)
    fn isotropic_twobody_energy(&self, distance_squared: f64) -> f64 {
        coulomb::TO_CHEMISTRY_UNIT / f64::from(self.permittivity)
            * self
                .scheme
                .ion_ion_energy(self.charge_product, 1.0, distance_squared.sqrt())
    }
}

impl<T: MultipoleEnergy + Cutoff> Cutoff for IonIon<T> {
    fn cutoff(&self) -> f64 {
        self.scheme.cutoff()
    }
    fn lower_cutoff(&self) -> f64 {
        self.scheme.lower_cutoff()
    }
}

/// Alias for ion-ion with Yukawa
pub type IonIonYukawa = IonIon<coulomb::pairwise::Yukawa>;

/// Alias for ion-ion with a plain Coulomb potential that can be screened
pub type IonIonPlain = IonIon<coulomb::pairwise::Plain>;

/// Ion-ion interaction with added ion-induced dipole energy
#[derive(Clone, PartialEq, Debug)]
#[cfg_attr(feature = "serde", derive(Serialize))]
pub struct IonIonPolar<T: MultipoleEnergy> {
    /// The underlying ion-ion interaction
    pub ionion: IonIon<T>,
    /// Charges of two particles
    charges: (f64, f64),
    /// Common excess polarizabilities of the ion in ų
    polarizabilities: (f64, f64),
}

impl<T: MultipoleEnergy> IonIonPolar<T> {
    /// Create a new ion-ion interaction with polarizability
    pub const fn new(ionion: IonIon<T>, charges: (f64, f64), polarizabilities: (f64, f64)) -> Self {
        Self {
            ionion,
            charges,
            polarizabilities,
        }
    }
}

impl<T: MultipoleEnergy + Debug + Clone + PartialEq + Send + Sync> IsotropicTwobodyEnergy
    for IonIonPolar<T>
{
    /// Calculate the isotropic twobody energy (kJ/mol)
    ///
    fn isotropic_twobody_energy(&self, distance_squared: f64) -> f64 {
        let r = distance_squared.sqrt();
        let scheme = &self.ionion.scheme;
        let ion_ion = scheme.ion_ion_energy(self.ionion.charge_product, 1.0, r);

        let rv = [r, 0.0, 0.0];
        let neg_rv = [-r, 0.0, 0.0];
        // These terms are always <= 0
        // TODO: This could be optimized by calling `ion_induced_dipole_energy` only once
        // with e.g. alpha=1 and charge=`q1*a0 + q0*a1`.
        let ion_induced_dipole =
            scheme.ion_induced_dipole_energy(self.charges.0, self.polarizabilities.1, rv)
                + scheme.ion_induced_dipole_energy(self.charges.1, self.polarizabilities.0, neg_rv);

        let to_kjmol = coulomb::TO_CHEMISTRY_UNIT / f64::from(self.ionion.permittivity);
        to_kjmol * (ion_ion + ion_induced_dipole)
    }
}

impl<T: MultipoleEnergy + Cutoff> Cutoff for IonIonPolar<T> {
    fn cutoff(&self) -> f64 {
        self.ionion.cutoff()
    }
    fn lower_cutoff(&self) -> f64 {
        self.ionion.lower_cutoff()
    }
}

impl<T: MultipoleEnergy + Display> Display for IonIonPolar<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(
            f,
            "IonIonPolar({}, {:?})",
            self.ionion, self.polarizabilities
        )
    }
}

// Test ion-ion energy
#[cfg(test)]
mod tests {
    use core::f64;

    use approx::assert_relative_eq;

    use super::*;
    use coulomb::{pairwise::Plain, DebyeLength};

    #[test]
    fn test_ion_ion() {
        let permittivity = ConstantPermittivity::new(80.0);
        let r: f64 = 7.0;
        let cutoff = f64::INFINITY;
        let scheme = Plain::new(cutoff, None);
        let ionion = IonIon::new(1.0, permittivity, scheme);
        let unscreened_energy = ionion.isotropic_twobody_energy(r.powi(2));
        assert_relative_eq!(unscreened_energy, 2.48099031507825);
        let debye_length = 30.0;
        let scheme = Plain::new(cutoff, Some(debye_length));
        let ionion = IonIon::new(1.0, permittivity, scheme);
        let screened_energy = ionion.isotropic_twobody_energy(r.powi(2));
        assert_relative_eq!(
            screened_energy,
            unscreened_energy * (-r / debye_length).exp()
        );
    }
    #[test]
    fn test_ion_ion_polar() {
        let permittivity = ConstantPermittivity::new(80.0);
        let r: f64 = 8.0;
        let charges = (1.0, -1.0);
        let cutoff = f64::INFINITY;
        let polarizabilities = (100.0, 80.0); // Excess polarizability in ų

        // No salt screening
        let scheme = Plain::new(cutoff, None);
        let ionion = IonIon::new(charges.0 * charges.1, permittivity, scheme);
        let ionion_polar = IonIonPolar::new(ionion.clone(), charges, polarizabilities);
        let energy = ionion_polar.isotropic_twobody_energy(r.powi(2));
        assert_relative_eq!(energy, -2.5524641571630236);

        let induced_energy = energy - ionion.isotropic_twobody_energy(r.powi(2));
        assert_relative_eq!(induced_energy, -0.38159763146955505);
        assert_relative_eq!(
            induced_energy,
            -(100.0 + 80.0) * coulomb::TO_CHEMISTRY_UNIT
                / (2.0 * f64::from(permittivity) * r.powi(4))
        );

        // With salt screening
        let scheme = Plain::new(cutoff, Some(30.0));
        let ionion = IonIon::new(charges.0 * charges.1, permittivity, scheme.clone());
        let ionion_polar = IonIonPolar::new(ionion.clone(), charges, polarizabilities);
        let energy = ionion_polar.isotropic_twobody_energy(r.powi(2));
        assert_relative_eq!(energy, -2.021903629249571);

        let induced_energy = energy - ionion.isotropic_twobody_energy(r.powi(2));
        let kappa = 1.0 / scheme.debye_length().unwrap();
        assert_relative_eq!(induced_energy, -0.3591754384137349);
        assert_relative_eq!(
            induced_energy,
            -(polarizabilities.0 + polarizabilities.1) * coulomb::TO_CHEMISTRY_UNIT
                / (2.0 * f64::from(permittivity))
                * (f64::exp(-r * kappa) * (1.0 / r.powi(2) + kappa / r)).powi(2),
            epsilon = 1e-7
        );
        assert_relative_eq!(
            induced_energy,
            -(polarizabilities.0 + polarizabilities.1) * coulomb::TO_CHEMISTRY_UNIT
                / (2.0 * f64::from(permittivity))
                * f64::exp(-2.0 * r * kappa)
                * (1.0 / r.powi(2) + kappa / r).powi(2),
            epsilon = 1e-7
        );
    }
}